Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30° and 60° with respect to the horizontal respectively as shown in figure. The speed of A is . At time t = 0s, an observer in A finds B at a distance of 500 m. This observer sees B moving with a constant velocity perpendicular to the line of motion of A. If at t = t0, A just escapes being hit by B, t0 in seconds is :

Engineering

Physics

Relative Motion

Question

Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30° and 60° with respect to the horizontal respectively as shown in figure. The speed of A is $100 \sqrt{3} {ms}^{- 1}$ . At time t = 0s, an observer in A finds B at a distance of 500 m. This observer sees B moving with a constant velocity perpendicular to the line of motion of A. If at t = t₀, A just escapes being hit by B, t₀ in seconds is :

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$V_{BA} = {\vec{V}}_{B} - {\vec{V}}_{A}$

⇒ v cos 30° $= 100 \sqrt{3}$

⇒ v = 200 m/s

V_BA = v sin 30° = 100 m/s

t = S_BA/V_BA = 5 sec.